Question

Two observers who are 2 miles apart on a horizontal plane observe a balloon in a same vertical plane with themselves. the angles of elevation are 50 degrees and 65 degrees respectively. find the height of the balloon,(a)if it is between the observers;(b)if it is on the same side of both of them

Answer 1

a)
angle up at top = 180 - 65 - 50 = 65
oh, my, this is an isosceles triangle, interesting

anyway
let's find the other two sides for fun
sin 50/a = sin 65/2
a = 2 sin 50/sin 65 = 1.69
and
b = 2 sin 65/sin 65 = 2 obviously


sin 65 = h/1.77
h = 1.69 sin 65 = 1.53
or alternatively
sin 50 = h/2
h = 2 sin 50 = 1.53 (whew! same answer :)

Answer 2

b) outside triangle is 50, 115 and 15
so
sin 15/2 = sin 115/a
a = 7 (long slant side)
then
sin 50 = h/7
h = 5.36

Answer 3

Wow that was fast! Thank you so much! :)

Answer 4

You are welcome.

Answer 5

how did you get the angles in b.)?

Answer 6

I drew a sketch

Between the steep slope (65 degrees) and horizontal outside it is 180 - 65 = 115
then up at the top of the outside triangle
180 - 115 - 50 = 15

Answer 7

Oh ok!
but I can't seem to understand the
"sin 50 = h/7
h = 5.36"
part. Is that a formula of getting the height?

Answer 8

Yes, right triangle, 7 is hypotenuse, h is opposite the 50 degrees

Answer 9

What is then the answer?

Answer 10

can u pls draw an illustration on the second problem? thanks!